Problem: Simplify the following expression: $ q = \dfrac{k - 8}{2k - 5} + 7 $
In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{2k - 5}{2k - 5}$ $ \dfrac{-7}{1} \times \dfrac{2k - 5}{2k - 5} = \dfrac{-14k + 35}{2k - 5} $ Therefore $ q = \dfrac{k - 8}{2k - 5} - \dfrac{-14k + 35}{2k - 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{k - 8 - (-14k + 35) }{2k - 5} $ Distribute the negative sign: $q = \dfrac{k - 8 + 14k - 35}{2k - 5}$ $q = \dfrac{15k - 43}{2k - 5}$